Luni, 30 iul 2007 01:49
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25
Problem: To Catch a Deer in the woods
1. Mathematical Methods
-----------------------
1.1 The Hilbert (axiomatic) method
----------------------------------
We place a locked cage onto a given point in the woods. After that
we introduce the following logical
system:
Axiom 1: The set of deers in the woods is not empty.
Axiom 2: If there exists a deer in the woods, then there exists a deer in the
cage.
Procedure: If P is a theorem, and if the following is holds:"P implies Q",
then Q is a theorem.
Theorem 1: There exists a deer in the cage.
1.2 The geometrical inversion method
------------------------------------
We place a spherical cage in the woods, enter it and lock it from inside. We
then perform an inversion with
respect to the cage. Then the deer is inside the cage, and we are outside.
1.3 The projective geometry method
----------------------------------
Without loss of generality we can view the woods as a plane surface. We
project the surface onto a line and
afterwards the line onto an interior point of the cage. Thereby the deer is
mapped onto that same point.
1.4 The Bolzano-Weierstrass method
----------------------------------
Divide the woods by a line running from north to south. The deer is then
either in the eastern or in the western
part. Lets assume it is in the eastern part. Divide this part by a line
running from east to west. The deer is either in
the northern or in the southern part. Lets assume it is in the northern
part. We can continue this process
arbitrarily and thereby constructing with each step an increasingly narrow
fence around the selected area. The
diameter of the chosen partitions converges to zero so that the deer is
caged into a fence of arbitrarily small
diameter.
1.5 The set theoretical method
------------------------------
We observe that the woods is a separable space. It therefore contains an
enumerable dense set of points
which constitutes a sequence with the deer as its limit. We silently
approach the deer in this sequence, carrying
the proper equipment with us.
1.6 The Peano method
--------------------
In the usual way construct a curve containing every point in the woods. It
has been proven [1] that such a curve
can be traversed in arbitrarily short time.
Now we traverse the curve, carrying a rifle, in a time less than what it
takes the deer to move a distance equal to
its own length.
1.7 A topological method
------------------------
We observe that the deer possesses the topological gender of a torus. We
embed the woods in a four
dimensional space. Then it is possible to apply a deformation [2] of
such a kind that the deer when returning
to the three dimensional space is all tied up in itself. It is then
completely helpless.
1.8 The Cauchy method
---------------------
We examine a deer-valued function f(z). Be \zeta the cage. Consider the
integral /
1 I f(z)
------- I --------- dz
2 \pi i I z - \zeta
/
C
where C represents the boundary of the woods. Its value is f(zeta), i.e.there
is a deer in the cage [3].
1.9 The Wiener-Tauber method
----------------------------
We obtain a tame deer, D_0, from the class D(-\infinity,\infinity),whose
fourier transform vanishes nowhere.
We put this deer somewhere in the woods.
D_0 then converges toward our cage. According to the general
Wiener-Tauber theorem [4] every other
deer D will converge toward the same cage.
(Alternatively we can approximate D arbitrarily close by translating D_0
through the woods [5].)
2 Theoretical Physics Methods
-----------------------------
2.1 The Dirac method
--------------------
We assert that wild deers can ipso facto not be observed in the woods.
Therefore, if there are any deers at all in the woods, they are tame. We
leave catching a tame deer as an exercise to the reader.
2.2 The Schroedinger method
---------------------------
At every instant there is a non-zero probability of the deer being in the
cage. Sit and wait.
2.3 The nuclear physics method
------------------------------
Insert a tame deer into the cage and apply a Majorana exchange operator [6]
on it and a wild deer.
As a variant let us assume that we would like to catch (for argument's sake)
a male deer. We insert a tame female deer into the cage and apply the
Heisenberg exchange operator [7], exchanging spins.
2.4 A relativistic method
-------------------------
All over the woods we distribute deer bait containing large amounts of
the companion star of Sirius. After enough of the bait has been eaten we
send a beam of light through the woods. This will curl around the deer so it
gets all confused and can be approached without being alerted to our
presence.
2.5 The Newton method
-----------------
Neglect friction and the deer and the cage will attract each other.
3 Experimental Physics Methods
------------------------------
3.1 The thermodynamics method
-----------------------------
We construct a semi-permeable membrane which lets everything but deers pass
through. This we drag through the woods.
3.2 The atomic fission method
-----------------------------
We irradiate the woods with slow neutrons. The deer becomes radioactive and
starts to disintegrate. Once the disintegration process is progressed far
enough the deer will be unable to resist.
:))
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